On Alternating 6-Cycles in Edge-Coloured Graphs
Combinatorics
2025-05-16 v1 Discrete Mathematics
Abstract
In this short note, we use flag algebras to prove that the number of colour alternating 6-cycles in a red/blue colouring of a large clique is asymptotically maximized by a uniformly random colouring. This settles the first open case of a problem of Basit, Granet, Horsley, K\"undgen and Staden.
Keywords
Cite
@article{arxiv.2505.09809,
title = {On Alternating 6-Cycles in Edge-Coloured Graphs},
author = {Hao Chen and Jonathan A. Noel},
journal= {arXiv preprint arXiv:2505.09809},
year = {2025}
}
Comments
19 pages, 2 figures